I’m using SymPy to calculate an integral involving trigonometric functions and parameters, but it returns the integral in its unevaluated form.

Here’s the Python code snippet from my Jupyter Notebook:

from sympy import symbols, cos, integrate, pi

x, a, b = symbols('x a b')
expr = -( (1 - cos(x))) / ((a + b - b * cos(x)))
integrate_result = integrate(expr, (x, 0, 2 * pi))
integrate_result.doit()

1. Why does SymPy not evaluate this integral?
2. Are there any tricks or methods to coax SymPy into computing a result for this type of integral?
3. Could the issue be related to the complexity of the expression or the use of parameters in the trigonometric functions?

Any insights or guidance on how to get SymPy to evaluate this integral would be greatly appreciated!